|
| |
|
|
A008919
|
|
Numbers n such that n written backwards is a nontrivial multiple of n.
|
|
6
|
|
|
|
1089, 2178, 10989, 21978, 109989, 219978, 1099989, 2199978, 10891089, 10999989, 21782178, 21999978, 108901089, 109999989, 217802178, 219999978, 1089001089, 1098910989, 1099999989, 2178002178, 2197821978, 2199999978, 10890001089
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
There are 2*Fibonacci([(n-2)/2]) terms with n digits (this is essentially twice A103609). - N. J. A. Sloane, Mar 20 2013
|
|
|
REFERENCES
|
Leonard F. Klosinski and Dennis C. Smolarski, On the Reversing of Digits, Math. Mag., 42 (1969), 208-210.
R. Webster and G. Williams, On the Trail of Reverse Divisors: 1089 and All that Follow, Mathematical Spectrum, Applied Probability Trust, Sheffield, Vol. 45, No. 3, 2012/2013, pp. 96 - 102.
D. Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986.
|
|
|
LINKS
|
Table of n, a(n) for n=1..23.
Eric Weisstein's World of Mathematics, Reversal
|
|
|
FORMULA
|
If reverse(n) = k*n in base 10, then k = 1, 4 or 9 [Klosinski and Smolarski]. Hence A008919 is the union of A001232 and A008918. - David W. Wilson
|
|
|
MATHEMATICA
|
Reap[ Do[ If[ Reverse[ IntegerDigits[n]] == IntegerDigits[4*n], Print[n]; Sow[n]]; If[ Reverse[ IntegerDigits[n + 11]] == IntegerDigits[9*(n + 11)], Print[n + 11]; Sow[n + 11]], {n, 78, 2*10^10, 100}]][[2, 1]] (* Jean-François Alcover, Jun 19 2012, after David W. Wilson, assuming n congruent to 78 or 89 mod 100 *)
|
|
|
PROG
|
(Haskell)
a008919 n = a008919_list !! (n-1)
a008919_list = [x | x <- [1..],
let (x', m) = divMod (a004086 x) x, m == 0, x' > 1]
-- Reinhard Zumkeller, Feb 03 2012
|
|
|
CROSSREFS
|
Cf. A001232, A004086, A008918, A214927, A103609. Reversals are in A031877.
Sequence in context: A175698 A110819 A071685 * A110843 A023093 A001232
Adjacent sequences: A008916 A008917 A008918 * A008920 A008921 A008922
|
|
|
KEYWORD
|
nonn,base,nice,changed
|
|
|
AUTHOR
|
N. J. A. Sloane.
|
|
|
EXTENSIONS
|
Corrected and extended by David W. Wilson Aug 15 1996, Dec 15 1997.
|
|
|
STATUS
|
approved
|
| |
|
|
